ISBN: 3-540-63293-X
TITLE: The Red Book of Varieties and Schemes
AUTHOR: Mumford, David
TOC:

Preface to the Second Edition V 
Preface to the First Edition VII 
Table of Contents IX 
I. Varieties 1 
1. Some algebra 1 
2. Irreducible algebraic sets 5 
3. Definition of a morphism 11 
4. Sheaves and affi ne varieties 16 
5. Definition of prevarieties and morphisms 25 
6. Products and the Hausdorff Axiom 33 
7. Dimension 40 
8. The fibres of a morphism 48 
9. Complete varieties 54 
10. Complex varieties 57 
II. Preschemes 65 
1. Spec (R) 66 
2. The category of preschemes 77 
3. Varieties and preschemes 86 
4. Fields of definition 94 
5. Closed subpreschemes 103 
6. The functor of points of a prescheme 112 
7. Proper morphisms and finite morphisms 121 
8. Specialization 127 
III. Local Properties of Schemes 137 
1. Quasi-coherent modules 138 
2. Coherent modules 146 
3. Tangent cones 153 
4. Non-singularity and differentials 164 
5. tale morphisms 174 
6. Uniformizing parameters 183 
7. Non-singularity and the UFD property 187 
8. Normal varieties and normalization 196 
9. Zariski's Main Theorem 207 
10. Flat and smooth morphisms 214 
Appendix: Curves and Their Jacobians 225 
Lecture I: What is a Curve and How Explicitly 
Can We Describe Them? 229 
Lecture II: The Moduli Space of Curves: Definition, Coordinatization, 
and Some Properties 243 
Lecture III: How Jacobians and Theta Functions Arise 257 
Lecture IV: The Torelli Theorem and the Schottky Problem 271 
Survey of Work on the Schottky Problem up to 1996 
by Enrico Arbarello 287 
References: The Red Book of Varieties and Schemes 293 
Guide to the Literature and References: 
Curves and Their Jacobians 294 
Supplementary Bibliography on the Schottky Problem 
by Enrico Arbarello 301 
END
